Table of Contents |
When establishing a linear relationship, you must first be given some information. This may be from a scenario, a graph, or sometimes even both are provided!
EXAMPLE
You are planning a road trip from St. Louis, Missouri to Las Vegas, Nevada. You look up the distance between the two cities, and estimate it to be 1600 miles. Since most of the trip will be on the open road, you also assume an average speed of 70 miles per hour.We might be able to answer some questions related to our scenario by using the graph, although our answers might be approximate rather than exact, due to the scale on both the x- and y-axes. We can develop an equation for the line on the graph, and then use the equation to solve for exact answers algebraically.
EXAMPLE
Write a linear equation for the scenario and graph from above.Using slope intercept form, substitute the value of 0 in for b because the y-intercept is at (0, 0). | |
Substitute the slope of 70 in for m | |
Simplify | |
Our solution |
Once you have an equation for a scenario, you can use this to answer some problems related to the situation.
EXAMPLE
The road trip is too much for one day. You figure that on your first day on the road, you can drive for about 6 hours. How many miles do you plan on driving on your first day?Using our equation, substitute 6 in for x | |
Multiply 70 and 6 | |
Our Solution |
EXAMPLE
The total distance for your road trip is 1600 miles. How many hours will you spend on the road to get from St. Louis to Las Vegas?Using our equation, substitute 1600 in for y | |
Divide both sides by 70 | |
Convert into a decimal | |
Our solution (rounded) |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License